Continuous-Discrete Path Integral Filtering
A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2009-08-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/11/3/402/ |
| _version_ | 1811301622870966272 |
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| author | Bhashyam Balaji |
| author_facet | Bhashyam Balaji |
| author_sort | Bhashyam Balaji |
| collection | DOAJ |
| description | A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of the path integral formula is demonstrated via some nontrivial examples. Specifically, it is shown that the simplest approximation of the path integral formula for the fundamental solution of the FPKfe can be applied to solve nonlinear continuous-discrete filtering problems quite accurately. The Dirac-Feynman path integral filtering algorithm is quite simple, and is suitable for real-time implementation. |
| first_indexed | 2024-04-13T07:12:10Z |
| format | Article |
| id | doaj.art-3486939c93f043c6a3e1cbb476f6202b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T07:12:10Z |
| publishDate | 2009-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3486939c93f043c6a3e1cbb476f6202b2022-12-22T02:56:50ZengMDPI AGEntropy1099-43002009-08-0111340243010.3390/e110300402Continuous-Discrete Path Integral FilteringBhashyam BalajiA summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of the path integral formula is demonstrated via some nontrivial examples. Specifically, it is shown that the simplest approximation of the path integral formula for the fundamental solution of the FPKfe can be applied to solve nonlinear continuous-discrete filtering problems quite accurately. The Dirac-Feynman path integral filtering algorithm is quite simple, and is suitable for real-time implementation.http://www.mdpi.com/1099-4300/11/3/402/Fokker-Planck equationKolmogorov equationuniversal nonlinear filteringFeynman path integralspath integral filteringdata assimilationtrackingcontinuousdiscrete filtersnonlinear filteringDirac-Feynman approximation |
| spellingShingle | Bhashyam Balaji Continuous-Discrete Path Integral Filtering Entropy Fokker-Planck equation Kolmogorov equation universal nonlinear filtering Feynman path integrals path integral filtering data assimilation tracking continuousdiscrete filters nonlinear filtering Dirac-Feynman approximation |
| title | Continuous-Discrete Path Integral Filtering |
| title_full | Continuous-Discrete Path Integral Filtering |
| title_fullStr | Continuous-Discrete Path Integral Filtering |
| title_full_unstemmed | Continuous-Discrete Path Integral Filtering |
| title_short | Continuous-Discrete Path Integral Filtering |
| title_sort | continuous discrete path integral filtering |
| topic | Fokker-Planck equation Kolmogorov equation universal nonlinear filtering Feynman path integrals path integral filtering data assimilation tracking continuousdiscrete filters nonlinear filtering Dirac-Feynman approximation |
| url | http://www.mdpi.com/1099-4300/11/3/402/ |
| work_keys_str_mv | AT bhashyambalaji continuousdiscretepathintegralfiltering |